Question: Solve for $x$ and $y$ using elimination. ${2x-2y = -12}$ ${3x+2y = 17}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $5x = 5$ $\dfrac{5x}{{5}} = \dfrac{5}{{5}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x-2y = -12}\thinspace$ to find $y$ ${2}{(1)}{ - 2y = -12}$ $2-2y = -12$ $2{-2} - 2y = -12{-2}$ $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ You can also plug ${x = 1}$ into $\thinspace {3x+2y = 17}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ + 2y = 17}$ ${y = 7}$